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Solve for $x$ : $x^2+49=0$

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Solve equations with variable exponents

Full solution

Q. Solve for

x

:

x^2+49=0

Isolate $x^2$ term: Isolate the $x^2$ term by subtracting $49$ from both sides of the equation. $\newline$ $x^2 + 49 - 49 = 0 - 49$ $\newline$ $x^2 = -49$
Take square root: Take the square root of both sides of the equation to solve for $x$ . Remember that taking the square root of a number yields both a positive and negative solution. $\newline$ $\sqrt{x^2} = \pm\sqrt{-49}$ $\newline$ $x = \pm\sqrt{-49}$
Recognize imaginary number: Recognize that the square root of a negative number involves an imaginary number. The square root of $-1$ is defined as the imaginary unit $i$ . $\newline$ $x = \pm\sqrt{49} * \sqrt{-1}$ $\newline$ $x = \pm7i$

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